The HCF of 27 and 36 is 9. In Maths, the full form of HCF is the Highest Common Factor. It is also called the Greatest Common Divisor (GCD). To find the HCF of given numbers easily, students can follow the article HCF of Two Numbers designed by BYJU’S experts. By utilising this article on a daily basis, students can solve complex problems relying on HCF with speed and correctness. In this article, let us learn the easy methods of how to determine the Highest Common Factor of 27 and 36, along with solved examples and FAQs in a comprehensive manner.
What is the HCF of 27 and 36?
The Highest Common Factor of 27 and 36 is 9. The factors of 27 and 36 are 1, 3, 9, 27 and 1, 2, 3, 4, 6, 9, 12, 18, 36, respectively. Here, the Greatest Common Factor (GCF) of 27 and 36 is 9.
How to Find HCF of 27 and 36?
There are three methods to find the HCF of 27 and 36:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 27 and 36 by Prime Factorisation Method
In the prime factorisation, to verify the HCF, we express the given numbers as the product of prime factors. Hence, 27 and 36 can be expressed as;
27 = 3 × 3 × 3
36 = 2 × 2 × 3 × 3
Common prime factors of 27 and 36 are 3 and 3.
Therefore,
HCF (27, 36) = 3 × 3 = 9
HCF of 27 and 36 by Long Division Method
We can determine the HCF of 27 and 36 by using the following steps:
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not zero, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor will be the HCF of the given two numbers.
For 27 and 36, the HCF by the long division method is;
Hence, HCF (27, 36) = 9
HCF of 27 and 36 by Listing the Factors
In this method, we find the HCF of 27 and 36 by listing out the common factors. The factors of 27 and 36 are given below:
Factors of 27: 1, 3, 9, 27
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Hence, HCF (27, 36) = 9
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Solved Example
Question: What is the HCF of 27 and 36 if their LCM is 108?
Solution: Given
LCM = 108
We know that
LCM × HCF = 27 × 36
HCF (27, 36) = (27 × 36) / LCM
HCF (27, 36) = (27 × 36) / 108
HCF (27, 36) = 972 / 108 = 9
Hence, the HCF of 27 and 36 is 9.
Frequently Asked Questions on HCF of 27 and 36
What is the HCF of 27 and 36?
Is the HCF of 27 and 36 the same as the HCF of 9 and 27?
Which of the following is the HCF of 27 and 36? 11, 18, 9, 20.
Mention the methods used to find the HCF of 27 and 36.
The following methods are used to find the HCF of 27 and 36
Prime Factorisation
Long Division method
Listing common factors
If the HCF of 27 and 36 is 9. What is the LCM?
We know that
HCF × LCM = 27 × 36
Given
HCF = 9
9 × LCM = 27 × 36
LCM = 108
Therefore the LCM is 108
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